Trajectories on Real Hypersurfaces of Type (A) and Those on a Complex Projective Space

Abstract

We study trajectories for Sasakian magnetic fields on a real hypersurface of type (A) in a complex projective space which can be seen as trajectories for some Kähler magnetic fields on the ambient space. In particular, when a real hypersurface is of type $({\rm A}_2)$, since the set of congruence classes of trajectories for a given Sasakian magnetic field is shown as an upper half disk in a Euclidean plane, in general, we investigate how the set of congruence classes of such special trajectories is included in this upper half disk.